4.45 g of H2SO4 was dissolved in 82.2 ml of water. The density of the solution was found to be 1.02 g/ml at 25°C. Calculate: i) the percentage (w/w) and ii) the mole fraction of bo... 4.45 g of H2SO4 was dissolved in 82.2 ml of water. The density of the solution was found to be 1.02 g/ml at 25°C. Calculate: i) the percentage (w/w) and ii) the mole fraction of both acid and water. Read more

Steps to Solve

1. Calculate the total mass of the solution

To find the total mass, we need to add the mass of the sulfuric acid to the mass of the water.

• Mass of water = volume of water × density of water
• Volume of water = 82.2 mL
• Density of water = 1.00 g/mL (approximate at 25°C)

Calculating the mass of water:

$$ \text{Mass of water} = 82.2 , \text{mL} \times 1.00 , \text{g/mL} = 82.2 , \text{g} $$

Now, add the mass of sulfuric acid to this mass:

$$ \text{Total mass} = 4.45 , \text{g} + 82.2 , \text{g} = 86.65 , \text{g} $$

2. Calculate the percentage by weight (w/w) of H2SO4

To calculate the weight percentage of the sulfuric acid in the solution, use the formula:

$$ \text{Percentage (w/w)} = \left( \frac{\text{mass of solute}}{\text{total mass}} \right) \times 100 $$

Plugging in the values:

$$ \text{Percentage (w/w)} = \left( \frac{4.45 , \text{g}}{86.65 , \text{g}} \right) \times 100 \approx 5.14% $$

3. Calculate the number of moles of H2SO4 and water

To determine the mole fraction, we first need to calculate the number of moles of each component.

• Molar mass of H2SO4 = 98.08 g/mol
• Molar mass of water (H2O) = 18.02 g/mol

For H2SO4:

$$ n_{\text{H2SO4}} = \frac{4.45 , \text{g}}{98.08 , \text{g/mol}} \approx 0.0454 , \text{mol} $$

For water:

$$ n_{\text{water}} = \frac{82.2 , \text{g}}{18.02 , \text{g/mol}} \approx 4.56 , \text{mol} $$

4. Calculate the mole fraction of H2SO4 and water

Mole fraction of a component is given by the formula:

$$ \text{Mole fraction} = \frac{\text{moles of component}}{\text{total moles}} $$

First, calculate the total moles:

$$ n_{\text{total}} = n_{\text{H2SO4}} + n_{\text{water}} = 0.0454 , \text{mol} + 4.56 , \text{mol} \approx 4.6054 , \text{mol} $$

Now, calculate the mole fractions:

• Mole fraction of H2SO4:

$$ X_{\text{H2SO4}} = \frac{n_{\text{H2SO4}}}{n_{\text{total}}} = \frac{0.0454}{4.6054} \approx 0.00985 $$

• Mole fraction of water:

$$ X_{\text{water}} = \frac{n_{\text{water}}}{n_{\text{total}}} = \frac{4.56}{4.6054} \approx 0.99015 $$